Solutions Problem Set 1
Macro III (14.453)
First of all a short note on the preferences we have.
1
h
i
vt = (1 )c + (Et vt+1 )
t
Note that in that case we no longer restrict (as in the usual framework) the
coecient of risk aversion to be inversely relate
14.453: Problem Set #2
Ivn Werning
a
1
Perfect Risk Sharing
Consider a nite group I of individuals. Income for each individual is determined each
i
period as a function of the current state of nature1 st S (where S is a nite set): yt (st ).
i
Denote aggre
Problem Set #3
Macroeconomic Theory III
1
Precautionary Savings in General Equilibrium
Let utility be given by:
X t
u (ct )
t=0
where u (c) = exp cfw_c . Assume the standard intertemporal budget con
straint
At+1 = (1 + r) (At + yt ct ) .
(note: we do not
Solutions Problem Set 3
Macro I I I (14.453)
QN P r oblem 1: i
N n i
N
HI t N w
Q
a K K
QK
a+ 1 ] HQ K I Ha K I Z
]
t , a
a ]
QK
Q
cfw_ K Z
r
Q
QK
cfw_ K ]
Q
QK
cfw_1 K 1 K 1 1 [
HQ K I
QK
Q
QK
HQ K I2
QK
cfw_ K ]
1 K
QK
] HQ K I K
14.454 - Macroeconomic Crisis
Problem set 1
Juan Pablo Xandri Antuna
04/15/2011
1
Question 1 - Kocherlakota (2000)
Take an economy with a representative, innitely-lived consumer. The consumer owns a technology
with which she produces output (Y ) using cap
Solutions PS4 Macro III
1
T wo-Sided L ack of Comm it ment : St at ionar y
A llocat ions
w
v1
v2
] 1 K v 1 K HQ I v 2
] 2 K v 2 K HQ I v 1
L v 2 H[ I ] v 1 H[ IN
a
v 1 K v 2 ] 1 K 2 K v 1 K v 2
v1 Kv2 ]
Q 1
K 2 Z
Q
p v 1
Q 1
v1 ] 1 K v1
Problem Set #1
Macroeconomic Theory III
Everyone should turn in their own problem set. You are encouraged to
work with a group. If you do please indicate all the members of your group.
1
Intertemporal Elasticity of Substitution, Risk
Aversion and the Cost
14.453: Problem Set
4
Ivn Werning
a
1
Incomplete Markets and Asset Prices
This problem investigates the eects of market incompleteness on asset pricing following
Constantinides and Due (1996). There is a continuum of individuals with identical CRRA
prefer
Solutions Problem Set 2
Macro III (14.453)
1. Problem 1: The general expression that can be derived for the CEQ-PIH
case for the change in consumption is:
t
X
1
[
1 + j=0 (1 + )j
=
t t+j
t1 t+j ]
so we only need to compute this expression for the dierent
Solutions toProblem Set # 4
Macro 453
October 18, 2003
1
Problem 1: Incomplete Markets and Asset
Prices
This problem investigates the eects of market incompleteness on asset pricing following Constantinides and Due (1996). There is a continuum of
individu
Problem Set #2
Macroeconomic Theory III
1
Marginal Propensity to Consume out of
Current Income
Consider the CEQPIH consumption function which leads to the random
walk representation for consumption.
Consider the following income processes: (t has Et1 t =